Inverter control apparatus and control method thereof

ABSTRACT

An inverter control apparatus and a control method thereof are provided. The inverter control apparatus and a control method thereof stably operate a three-phase motor using a capacitor having a small capacitance for a DC link. The inverter control apparatus includes a current sensor to sense an output current of the inverter, a voltage sensor to sense a DC-link voltage of the inverter, and a controller to generate an average of a periodically varying rotor based q-axis current boundary value based on the output current and the DC-link voltage to generate a current reference on the basis of the average of the rotor based q-axis current boundary value, and to drive a three-phase motor based on the current reference. Stabilized variable speed control of a motor by using a small-capacitance capacitor for a DC link of an inverter is performed and reliability of an inverter circuit improved.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to, and claims priority to, Korean PatentApplication No. 2012-81486, filed on Jul. 25, 2012 in the KoreanIntellectual Property Office, the disclosure of which is incorporatedherein by reference.

BACKGROUND

1. Field

Embodiments of the present invention relate to an inverter controlapparatus and a control method thereof and, more particularly, to aninverter control apparatus and a control method thereof to stablyoperate a three-phase motor using a capacitor having a small capacitancefor a DC link.

2. Description of the Related Art

FIG. 1 illustrates a waveform of a conventional q-axis currentreference.

Referring to FIG. 1, a DC-link voltage waveform a1, a q-axis currentreference waveform a2 in a trapezoidal form, and a q-axis currentreference waveform a3 in a sine squared form are illustrated.

To stably operate a permanent magnet synchronous motor with an inverterusing a small-capacitance capacitor, it is important to generate a rotorbased q-axis current reference and a rotor based d-axis currentreference.

Rotor based q-axis current reference may be modulated into a sinesquared form and a rotor based q-axis current reference may be modulatedinto a trapezoidal form.

However, the method of modulating a rotor based q-axis current referenceinto a sine squared form does not consider a voltage drop due toinductance and stator resistance and needs an additional methodology formeasuring the voltage of input power, such as a voltage sensor.

The method of modulating a rotor based q-axis current reference into atrapezoidal form cannot eliminate harmonic components of an inputcurrent.

In conventional methods, the rotor based d-axis current reference uses avoltage equation (Equation 1) and voltage limit equation (Equation 2),or a d-axis current is controlled to have a negative value in a specificregion having an insufficient DC-link voltage.

$\begin{matrix}{{V_{ds}^{r} = {{R_{s}i_{ds}^{r}} + {L_{d}\frac{}{t}i_{ds}^{r}} - {\omega_{r}L_{q}i_{qs}^{r}}}}{V_{qs}^{r} = {{R_{s}i_{qs}^{r}} + {L_{q}\frac{}{t}i_{qs}^{r}} + {\omega_{r}( {{L_{d}i_{ds}^{r}} + \lambda_{pm}} )}}}} & \lbrack {{Equation}\mspace{14mu} 1} \rbrack \\{\frac{V_{dc}}{\sqrt{3}} \geq \sqrt{V_{ds}^{r*2} + V_{qs}^{r*2}}} & \lbrack {{Equation}\mspace{14mu} 2} \rbrack\end{matrix}$

However, when a small-capacitance capacitor may be used for a DC link ofan inverter, the DC link voltage of the inverter pulsates at double asource frequency, and thus a voltage limit circle varies even in asteady state. Accordingly, instantaneous change of the d-axis currentdeteriorates system stability.

SUMMARY

Additional aspects and/or advantages will be set forth in part in thedescription which follows and, in part, will be apparent from thedescription, or may be learned by practice of the invention.

It is an aspect of the present invention to provide a method to generatea rotor based q-axis current reference and a rotor based d-axis currentreference using an “average voltage limit circle” to reduce pulsation ofa DC link voltage.

It is an aspect of the present invention to provide a method to estimatea system frequency such that a rotor based q-axis current reference hasa sine squared form of the system frequency (source frequency) when thepower factor of input power needs to be controlled to be 1 to satisfyregulation of harmonics of input current.

In accordance with an aspect of the present invention, an invertercontrol apparatus is provided that controls an inverter having a DC-linkvoltage pulsating at double a system frequency, the inverter controlapparatus including a current sensor to sense an output current of theinverter, a voltage sensor to sense a DC-link voltage of the inverter,and a controller to generate the average of a periodically varying rotorbased q-axis current boundary value on the basis of the output currentand the DC-link voltage, to generate a current reference on the basis ofthe average of the rotor based q-axis current boundary value, and todrive a three-phase motor on the basis of the current reference.

The controller may include a velocity controller to generate an outputtorque command value on the basis of the output current; and a currentreference generator to generate the current reference corresponding tothe output torque command value.

The current reference generator may include a system angle estimator toestimate at least one of a system angle, a system frequency, a doublesystem angle and a double system frequency on the basis of the DC-linkvoltage.

The current reference generator may further include a q-axis currentreference generator to generate a rotor based q-axis current referencein a sine squared form, which is synchronized with the system angle, onthe basis of the system angle.

The current reference generator may include a d-axis current referencegenerator to calculate an average of the periodically varying rotorbased q-axis current boundary value and to generate a rotor based d-axiscurrent reference on the basis of the average of the rotor based q-axiscurrent boundary value and the rotor based q-axis current reference.

The system angle estimator may include a DC-link voltage squarecalculator to square the DC-link voltage to generate a DC-link voltagesquare, a band pass filter to generate a double system frequencycomponent value having a frequency twice the system frequency on thebasis of the DC-link voltage square and the double system frequency, aphase retarder to generate a 90° phase-retarded value having a phaseretarded by 90° from the double system frequency component value, afifth frame converter to generate a synchronous reference frame basedd-axis virtual voltage and a synchronous reference frame based q-axisvirtual voltage, which are constants and have a phase differencetherebetween, on the basis of the 90°-phase-retarded value, a valueobtained by multiplying the double system frequency component value by“−1”, and the double system angle, and a phase lock unit to generate atleast one of the system angle, the system frequency, the double systemangle, and the double system frequency on the synchronous referenceframe based d-axis virtual voltage and a constant value “0”.

The phase lock unit may include an all-pass filter or a secondarygeneral integrator to retard a phase.

The phase lock unit may include a phase lock loop to lock the phase of areceived signal and keep the frequency of an output signal uniform.

The q-axis current reference generator may include a sine squarecalculator to generate a unit sine square waveform having the systemangle, a q-axis current reference converter to generate a q-axis currentreference corresponding to the output torque command value, a firstmultiplier to multiply the unit sine square waveform by the q-axiscurrent reference to generate a q-axis current reference in a sinesquared form, a current gain setting unit to generate a current gainthat makes the average of the output torque command value equal to theaverage of a current reference modified torque generated according tothe rotor based q-axis current reference, and a second multiplier tomultiply the q-axis current reference in a sine squared form by thecurrent gain to generate a rotor based q-axis current reference.

The current gain setting unit may set the current gain to a value of“2”.

The d-axis current reference generator may include a current margincalculator to calculate the average of the periodically varying rotorbased q-axis current boundary value on the basis of the DC-link voltageand to generate a rotor based q-axis current margin value on the basisof the average of the rotor based q-axis current boundary value, acurrent margin reference unit to generate a rotor based q-axis currentmargin reference on the basis of the output torque command value, and afirst adder to generate an error value by subtracting the rotor basedq-axis current margin reference from the rotor based q-axis currentmargin value.

The current margin calculator may include a d-axis voltage boundaryvalue calculator to generate a rotor based d-axis voltage boundary valuecorresponding to a maximum instantaneous voltage that can be applied toa d axis on the basis of the DC-link voltage, a unit gain calculator togenerate a unit gain that changes a voltage value into a current value,a q-axis current boundary converter to generate a rotor based q-axiscurrent boundary value on the basis of the rotor based d-axis voltageboundary value and the unit gain, and a q-axis current margin calculatorto subtract the rotor based q-axis current reference from the average ofthe rotor based q-axis current boundary value to generate a rotor basedq-axis margin value.

The current margin reference unit may set the rotor based d-axis currentreference to a positive value such that the rotor based d-axis currentreference is set to a negative value when a generated torque isinsufficient due to current limitation.

The current margin reference unit may set the rotor based q-axis currentmargin reference to “0” in a steady state or when current is notlimited.

In accordance with an aspect of the present invention, a method tocontrol an inverter control apparatus that includes a current sensor, avoltage sensor and a controller and controls an inverter having aDC-link voltage pulsating at double a system frequency includes theinverter control apparatus sensing an output current and a DC-linkvoltage of the inverter, the inverter control apparatus calculating theaverage of a periodically varying rotor based q-axis current boundaryvalue on the basis of the output current and the DC-link voltage, theinverter control apparatus generating a current reference on the basisof the average of the rotor based q-axis current boundary value, and theinverter control apparatus driving a three-phase motor on the basis ofthe current reference.

The inverter control apparatus generating the current reference mayinclude estimating at least one of a system angle, a system frequency, adouble system angle and a double system frequency on the basis of theDC-link voltage.

The inverter control apparatus generating the current reference furthermay include generating a rotor based q-axis current reference in a sinesquared form, which is synchronized with the system angle, on the basisof the system angle.

The inverter control apparatus generating the current reference mayfurther include generating a rotor based d-axis current reference on thebasis of the average of the rotor based q-axis current boundary valueand the rotor based q-axis current reference.

The inverter control apparatus estimating at least one of the systemangle, the system frequency, the double system angle and the doublesystem frequency may include: squaring the DC-link voltage to generate aDC-link voltage square, generating a double system frequency componentvalue having a frequency twice the system frequency on the basis of theDC-link voltage square and the double system frequency, generating a 90°phase-retarded value having a phase retarded by 90° from the doublesystem frequency component value, generating a synchronous referenceframe based d-axis virtual voltage and a synchronous reference framebased q-axis virtual voltage, which are constants and have a phasedifference therebetween, on the basis of the 90°-phase-retarded value, avalue obtained by multiplying the double system frequency componentvalue by “−1”, and the double system angle, and generating at least oneof the system angle, the system frequency, the double system angle, andthe double system frequency on the synchronous reference frame basedd-axis virtual voltage and constant “0”.

The inverter control apparatus generating the rotor based q-axis currentreference may include: generating a unit sine square waveform having thesystem angle, generating a q-axis current reference corresponding to theoutput torque command value, multiplying the unit sine square waveformby the q-axis current reference to generate a q-axis current referencein a sine squared form, generating a current gain that makes the averageof the output torque command value equal to the average of a currentreference modified torque generated according to the rotor based q-axiscurrent reference, and multiplying the q-axis current reference in asine squared form by the current gain to generate a rotor based q-axiscurrent reference.

The current gain setting unit may set the current gain to a value of“2”.

The inverter control apparatus generating the rotor based d-axis currentreference may include: generating a rotor based d-axis voltage boundaryvalue corresponding to a maximum instantaneous voltage that can beapplied to a d axis on the basis of the DC-link voltage, generating aunit gain that changes a voltage value into a current value, generatinga rotor based q-axis current boundary value on the basis of the rotorbased d-axis voltage boundary value and the unit gain, subtracting therotor based q-axis current reference from the average of the rotor basedq-axis current boundary value to generate a rotor based q-axis marginvalue, generating a rotor based q-axis current margin reference on thebasis of the output torque command value, generating an error value bysubtracting the rotor based q-axis current margin reference from therotor based q-axis current margin value, and sequentially applying theerror value to a low pass filter and a proportional integrator togenerate a rotor based d-axis current reference.

The inverter control apparatus generating the rotor based d-axis currentreference may include setting the rotor based d-axis current referenceto a positive value such that the rotor based d-axis current referenceis set to a negative value when generated torque is insufficient due tocurrent limitation.

The inverter control apparatus generating the rotor based d-axis currentreference may include setting the rotor based q-axis current marginreference to “0” in a steady state or when current is not limited.

According to embodiments of the invention, it is possible to performstabilized variable speed control of a motor by using asmall-capacitance capacitor for a DC link of an inverter and to improvereliability of an inverter circuit. Furthermore, a circuit for initiallycharging a capacitor C an be eliminated using the small-capacitancecapacitor.

According to embodiments of the invention, an additional circuit forpower factor improvement can be removed by using a method to estimate asystem frequency.

As described above, according to embodiments of the invention, it ispossible to reduce costs and improve reliability of products bydecreasing the number of components.

BRIEF DESCRIPTION OF THE DRAWINGS

These and/or other aspects of the invention will become apparent andmore readily appreciated from the following description of theembodiments, taken in conjunction with the accompanying drawings ofwhich:

FIG. 1 illustrates the waveform of a conventional q-axis currentreference;

FIG. 2 illustrates an inverter control apparatus according to anembodiment of the present invention;

FIG. 3 illustrates a controller according to an embodiment of thepresent invention;

FIG. 4 illustrates a current reference generator according to anembodiment of the present invention;

FIG. 5A illustrates a system angle estimator according to an embodimentof the present invention;

FIG. 5B illustrates an input waveform and calculated waveforms of thesystem angle estimator according to an embodiment of the presentinvention;

FIG. 6A illustrates a rotor based q-axis current reference generatoraccording to an embodiment of the present invention;

FIG. 6B illustrates waveforms of an output torque command value and aq-axis current reference in a sine squared form according to anembodiment of the present invention;

FIG. 7A illustrates an average voltage limit circle and load torquecurves according to an embodiment of the present invention;

FIG. 7B illustrates a rotor based d-axis current reference generatoraccording to an embodiment of the present invention;

FIG. 7C illustrates a generation of a rotor based d-axis currentreference and a rotor based q-axis current reference;

FIG. 8 illustrates a method to control an inverter control apparatusaccording to an embodiment of the present invention;

FIG. 9 illustrates a method to generate rotor based d-axis and q-axiscurrent references according to an embodiment of the present invention;

FIG. 10 illustrates a method to estimate a system angle according to anembodiment of the present invention;

FIG. 11 illustrates a method to generate a q-axis current referenceaccording to an embodiment of the present invention;

FIG. 12 illustrates a method to generate a d-axis current referenceaccording to an embodiment of the present invention;

FIG. 13 illustrates a motor driving waveform when a compressor of a 1 kWair-conditioner is controlled at 5400 r/min according to an embodimentof the present invention;

FIG. 14 illustrates waveforms of the current and voltage of input poweraccording to an embodiment of the present invention; and

FIG. 15 illustrates an input current harmonics analysis result accordingto an embodiment of the present invention.

DETAILED DESCRIPTION

Reference will now be made in detail to the embodiments of the presentinvention, examples of which are illustrated in the accompanyingdrawings, wherein like reference numerals refer to like elementsthroughout.

FIG. 2 illustrates an inverter control apparatus according to anembodiment of the present invention.

The inverter control apparatus 1 according to an embodiment of thepresent invention drives a three-phase motor and controls an inverterhaving a DC-link voltage that pulsates at a frequency twice a systemfrequency and includes a current sensor, a voltage sensor and acontroller. The controller receives an inverter output current valuefrom the current sensor and accepts an inverter DC-link voltage valuefrom the voltage sensor to estimate a system angle or a systemfrequency. The controller generates a rotor based q-axis currentreference in a sine squared form, which is synchronized with the systemangle, averages a periodically varying voltage limit value for a halfcycle of the system frequency to generate an average q-axis currentvalue, and generates a rotor based q-axis current reference on the basisof the average q-axis current value.

A three-phase motor 45 may be a permanent magnet synchronous motor, butis not limited thereto.

A power supply unit 2 supplies single-phase AC power. The power supplyunit 2 may include a single-phase input power supply Vin and an internalinductor Ls.

A rectifier 3 may convert AC input from the power supply unit 2 to DC.The rectifier 3 can execute a rectification function of passing currentonly in one direction owing to small forward resistance and sufficientlylarge reverse resistance thereof. The rectifier 3 includes a full-bridgediode rectifier using 4 diodes D1 to D4.

A DC link 4 may include a capacitor C that stores a DC voltage convertedby the rectifier 3 and 2 resistors R1 and R2 connected in series.

The capacitor C can charge the DC voltage converted by the rectifier 3and discharge the charged DC voltage through the resistors R1 and R2.

A time taken to charge and discharge the DC voltage depends on thecapacitance of the capacitor C. That is, the time taken to discharge thevoltage increases as the capacitance of the capacitor C increases.

Accordingly, the capacitor C can smooth a half-wave-rectified voltagewaveform applied thereto when the capacitor C has a large capacitance.That is, the capacitor C can convert a ripple current with a varyingvoltage into a specific voltage.

However, the present invention provides a function of stably controllingthe three-phase motor 45 when the capacitor C has a small capacitance.

When the capacitor C has a small capacitance, the voltage charged in thecapacitor C has large pulsation because the voltage rapidly discharges.

In this case, the capacitor C has a capacitance of 5 μF to tens of μF.The capacitor may include a film capacitor.

An inverter constructed such that an electrolytic capacitor is not usedfor the DC link by reducing the capacitance of the DC-link capacitor Cto 5 to tens of μF from 1000 to thousands of μF is called a single-phaseelectrolytic capacitor-less inverter.

The rectified voltage Vdc has large pulsation because of thesmall-capacitance capacitor C. Accordingly, embodiments of the presentinvention can reduce harmonics of the input current and improve thepower factor by appropriately setting a switching signal.

The voltage charged in the capacitor C is applied to the 2 resistors R1and R2 connected in series to the capacitor C depending on the ratio ofthe 2 resistors R1 and R2 according to the voltage divider rule.

An inverter 5 can convert DC power to AC power. The inverter 5 canconvert the DC voltage stored in the DC link 4 to an AC voltage having afrequency and size depending on a load condition.

The inverter 5 includes 6 switches S1 to S6. The inverter 5 can generatethree-phase AC by turning on or off the 6 switches S1 to S6 when aswitch on or off signal is supplied thereto from a gate driver 8.

The switches S1 to S6 may include switching transistors used as circuitswitching elements.

Three-phase AC is AC with respect to three electromotive forces havingthe same frequency and different phases. In general, three-phase ACindicates AC flowing according to symmetrical three-phase electromotiveforces and includes three sinusoidal alternating currents having a phasedifference of 120° and the same amplitude.

The current sensor 6 can sense the output current of the inverter 5. Theoutput current of the inverter 5 is applied to the three-phase motor 45.

The current sensor 6 may use a 3-shunt or 1-shunt scheme in which ashunt resistor is added to lower switches and ground of the inverter 5.

The current sensor 6 can sense a three-phase motor (45) current (two orthree phases among a phase, b phase and c phase) and transmit a sensedoutput current value to the controller 9. Specifically, the currentsensor 6 can transmit the output current value to an A/D converter (notshown) of the controller 9.

The voltage sensor 7 can sense the voltage of the DC link 4. The voltagecharged in the capacitor C is applied to the resistors R1 and R2 of theDC link 4 and the voltage sensor 7 can detect the voltage charged in thecapacitor C by sensing a voltage applied to one of the resistors R1 andR2.

When the small-capacitance capacitor C is used, the voltage of thecapacitor C pulsates and the voltage sensor 7 can sense the pulsatingvoltage.

The voltage sensor 7 can sense the voltage of the DC link 4 and transmitthe sensed voltage value to the controller 7.

The gate driver 8 receives a switching control signal from thecontroller 9 and transmits a signal for turning the switches S1 to S6 onor off to the inverter 5.

The controller 9 receives information on the sensed current from thecurrent sensor 6, receives information on the sensed voltage from thevoltage sensor 7 and generates a rotor based q-axis current referenceand a rotor based d-axis current reference.

The controller 9 generates a switching signal for stably driving thethree-phase motor 45 using the rotor based q-axis current reference androtor based d-axis current reference and transmits the switching signalto the gate driver 8.

The controller 9 is described in detail.

FIG. 3 illustrates the controller according to an embodiment of thepresent invention.

A rest frame based on a stator and a synchronous reference framerotating at a synchronous speed may be used as a reference frame tosolve complexity of a time-varying differential equation included in thevoltage equation of an AC motor and to analyze a transient state.

In the following description, superscript “r” denotes rotor base(synchronous reference frame), superscript “s” denotes a stator base(rest frame), subscript “*” represents a reference, superscript “r*”represents a rotor base (synchronous frame) reference value, andsubscript “s” denotes a stator of a motor.

The controller 9 may include a rotor angular position estimator 10, arotor angular velocity estimator 20, an ND converter 30, a first frameconverter 40, a velocity controller 50, a current reference generator60, a current controller 70, a second frame converter 80, anover-modulator 90, a third frame converter 100, a fourth frame converter110, and an SVPWM modulator 120.

The rotor angular position estimator 10 can estimate the position of arotor without using a position sensor.

The rotor angular position estimator 10 can generate a rotor angularposition estimate 11 (θ_(r)).

The rotor angular velocity estimator 20 can generate a rotor angularvelocity estimate 21 (ω_(r)) by differentiating the rotor angularposition estimate 11 transmitted from the rotor angular positionestimator 10.

The A/D converter 30 can convert an analog signal to a digital signal.

The A/D converter 30 can receive an output phase current sense signal ofthe inverter 5, which is an analog signal, from the current sensor 6 andgenerate three-phase motor input phase current values 32, 33 and 34corresponding to digital signals.

The A/D converter 30 can receive a voltage sense signal of the DC link4, which corresponds to an analog signal, from the voltage sensor 7 andgenerate a DC-link voltage 36 corresponding to a digital signal.

In the following, it is assumed that the three-phase motor input phasecurrent values 32, 33 and 34 are received from the current sensor 6 andthe DC-link voltage 36 is received from the voltage sensor 7 forconvenience of description.

The first frame converter 40 frame-converts the three-phase motor inputphase current values 32, 33 and 34 to rotor based two-phase current 41and 42.

The first frame converter 40 receives the three-phase motor input phasecurrent values 32, 33 and 34 from the current sensor 6 and receives therotor angular position estimate 11 from the rotor angular positionestimator 10. The first frame converter 40 can generate the rotor basedd-axis current value 41 and the rotor based q-axis current value 42,which are constants having a phase difference of 90° therebetween.

The velocity controller 50 can receive a rotor angular velocityreference 51 from a main MCU of the system or generate the rotor angularvelocity reference 51. The velocity controller 50 can receive the rotorangular velocity estimate 21 from the rotor angular velocity estimator20.

The velocity controller 50 can generate an output torque command value53 corresponding to an angular velocity necessary for the rotor angularvelocity estimate 21 to track the rotor angular velocity reference 51.

The output torque command value 53 may be a value obtained bysubtracting an anti-wind up value corresponding to a torque generateddue to current limitation from an actually necessary torque.

The current reference generator 60 may receive the output torque commandvalue 53 from the velocity controller 50, receive a rotor based d-axisvoltage limit value 101 and a rotor based q-axis voltage limit value 102from the third frame converter 100, and accept the DC-link voltage 36from the voltage sensor 7.

The current reference generator 60 can generate a rotor based d-axiscurrent reference 61 and a rotor based q-axis current reference 62corresponding to the output torque command value 53.

The current reference generator 60 is described in detail.

The current controller 70 can receive the rotor based d-axis currentreference 61 and the rotor based q-axis current reference 62 from thecurrent reference generator 60 and receive the rotor based d-axiscurrent value 41 and the rotor based q-axis current value 42 from thefirst frame converter 40.

The current controller 70 can generate a rotor based d-axis voltagereference 71 and a rotor based q-axis voltage reference 72, whichrespectively correspond to the rotor based d-axis current reference 61and the rotor based q-axis current reference 62.

The second frame converter 80 can receive the rotor based d-axis voltagereference 71 and the rotor based q-axis voltage reference 72 from thecurrent controller 70 and accept the rotor angular position estimate 11from the rotor angular position estimator 10.

The second frame converter 80 can generate a stator based d-axis voltagereference 81 and a stator based q-axis voltage reference 82, which havea phase difference of 90° therebetween and respectively correspond tothe rotor based d-axis voltage reference 71 and the rotor based q-axisvoltage reference 72.

The over-modulator 90 can receive the stator based d-axis voltagereference 81 and the stator based q-axis voltage reference 82 from thesecond frame converter 80 and accept the DC-link voltage 36 from thevoltage sensor 7.

The over-modulator 90 can generate a stator based d-axis voltage limitvalue 91 and a stator based q-axis voltage limit value 92 whichrespectively correspond to the stator based d-axis voltage reference 81and the stator based q-axis voltage reference 82.

The third frame converter 100 can receive the stator based d-axisvoltage limit value 91 and the stator based q-axis voltage limit value92 from the over-modulator 90 and accept the rotor angular positionestimate 11 from the rotor angular position estimator 10.

The third frame converter 100 can generate the rotor based d-axisvoltage limit value 101 and the rotor based q-axis voltage limit value102 which have a phase difference of 90° therebetween and respectivelycorrespond to the stator based d-axis voltage limit value 91 and thestator based q-axis voltage limit value 92.

The fourth frame converter 110 can receive the stator based d-axisvoltage limit value 91 and the stator based q-axis voltage limit value92 from the over-modulator 70.

The fourth frame converter 110 can generate three-phase voltagereferences 111, 112 and 113 corresponding to three-phase AC.

The SVPWM modulator 120 can receive the three-phase voltage references111, 112 and 113 from the fourth frame converter 110 and accept therotor angular position estimator 11 from the rotor angular positionestimator 10.

The SVPWM modulator 120 can generate switching control signals 121 to126 for controlling the 6 switches (not shown) of the inverter 5, whichcorrespond to the three-phase voltage references 111, 112 and 113.

FIG. 4 illustrates a current reference generator according to anembodiment of the present invention.

The current reference generator 60 according to an embodiment of thepresent invention can take an error in motor parameters of the motorvoltage equation into account even if the current reference generator 60is not aware of the motor parameters, and provide a high-reliabilitycontrol method through system angle estimation.

Referring to FIG. 4, the current reference generator 60 includes asystem angle estimator 200, a q-axis current reference generator 300 anda d-axis current reference generator 400.

The system angle estimator 200 can receive the DC-link voltage 36 fromthe voltage sensor 7. The system angle estimator 200 can generate asystem angle 201, a system frequency 202, a double system angle 251 anda double system frequency 252.

The q-axis current reference generator 300 can receive the output torquecommand value 53 from the velocity controller (not shown) and accept thesystem angle 201 from the system angle estimator 200. The q-axis currentreference generator 300 can generate the rotor based q-axis currentreference 62 in a sine squared form, which is synchronized with thesystem angle.

The d-axis current reference generator 400 can receive the output torquecommand value 53 from the velocity controller, receive the DC-linkvoltage 36 from the voltage sensor 7, accept the rotor based q-axiscurrent reference 62 from the q-axis current reference generator 300,and accept the rotor based d-axis voltage limit value 101 and the rotorbased q-axis voltage limit value 102 from the third frame converter (notshown). The d-axis current reference generator 400 can receive the rotorbased d-axis current reference value 61 through feedback.

The d-axis current reference generator 400 can generate the rotor basedd-axis current reference 61.

FIG. 5A illustrates a system angle estimator.

The system angle estimator 200 can estimate the system angle 201 of theinput power voltage using the DC-link voltage 36 rather than measuringthe input power voltage using an additional voltage measurement sensor.

Referring to FIG. 5A, the system angle estimator 200 can receive theDC-link voltage 36 and generate the system angle 201, the systemfrequency 202, the double system angle 251 and the double systemfrequency 252.

The system angle estimator 200 may include a DC-link voltage squarecalculator 210, a band pass filter 220, a phase retarder 230, a fifthframe converter 240, and a phase lock unit 250.

The DC-link voltage square calculator 210 can receive the DC-linkvoltage 36 from the voltage sensor 7 and generate a DC-link voltagesquare 211. The DC-link voltage square 211 may be obtained by squaringthe DC-link voltage 36.

The band pass filter 220 can receive the DC-link voltage square 211 fromthe DC-link voltage square calculator 2100 and accept double systemfrequency 252 (2ω_(grid)) from the phase lock unit 250. The band passfilter 220 can generate a double system frequency component value 221(V_(dc) _(—) _(2ω) _(grid) ) of the DC-link voltage square 211.

The band pass filter 220 has a frequency twice the system frequency asthe center frequency thereof.

For example, the band pass filter 220 can set the frequency twice thesystem frequency (50 Hz or 60 Hz) to an initial value, and use thedouble system frequency 252 (2ω_(grid)) by feeding back the same incases other than a case in which the motor is driven.

The band pass filter 220 can perform a calculation according to Equation3.

V _(dc) _(—) _(2ω) _(grid) =BPF(V _(dc) ²,2ω_(grid))

In Equation 3, V_(dc) ² denotes the DC-link voltage square, ω_(grid)denotes the system frequency, and V_(dc) _(—) _(2ω) _(grid) representsthe double system frequency component value 221 of the DC-link voltagesquare 211, which is the voltage value after passing through the bandpass filter 220 having the double system frequency as the centerfrequency thereof.

When the DC-link voltage 36 is squared, a component cos 2θ_(E) exists inthe DC-link voltage square and this value can pass through the band passfilter 220 having the double system frequency as the center frequencythereof.

The phase retarder 230 can receive the double system frequency componentvalue 221 of the DC-link voltage square 211 from the band pass filter220. The phase retarder 230 can generate a 90° phase-retarded value 231(V_(dc) _(—) _(2ω) _(grid) (θ−90°)) having a phase retarded by 90° fromthe double system frequency component value 221.

The phase retarder 230 performs calculation according to Equation 4.

V _(dc) _(—) _(2ω) _(grid) (θ−90°)=SOGI(V _(dc) _(—) _(2ω) _(grid) )

or V _(dc) _(—) _(2ω) _(grid) (θ−90°)=APF(V _(dc) _(—) _(2ω) _(grid))  Equation 4

In Equation 4, V_(dc) _(—) _(2ω) _(grid) denoted the double systemfrequency component value 221 of the DC-link voltage square 211, SOGI(Second Order General Integrator) denotes a secondary generalintegrator, APF represents an all-pass filter, and V_(dc) _(—) _(2ω)_(grid) (θ−90°) represents the 90° phase-retarded value 231.

For example, the phase retarder 230 can include an all-pass filter or asecondary general integrator.

The fifth frame converter 230 can receive the 90° phase-retarded value231 from the phase retarder 230, receive a value obtained by multiplyingthe double system frequency component value 221 (V_(dc) _(—) _(2ω)_(grid) ) of the DC-link voltage square 211 by “−1” from the band passfilter 220, and accept the double system angle 251 (2θ_(g)) from thephase lock unit 250.

A stator based d-axis virtual voltage 231 (V_(dc) _(—) _(ds)) and astator based q-axis virtual voltage 232 (V_(dc) _(—) _(qs) ^(S)) can bedefined by Equation 5.

V _(dc) _(—) _(dc) ^(S) =V _(dc) _(—) _(2ω) _(grid) (θ−90°)

V _(dc) _(—) _(qs) ^(S) =−V _(dc) _(—) _(2ω) _(grid)   Equation 5

In Equation 5, V_(dc) _(—) _(ds) ^(S) denotes the stator based d-axisvirtual voltage 231 and V_(dc) _(—) _(2ω) _(grid) (θ−90°) denotes the90° phase-retarded value 231. The stator based d-axis virtual voltage231 and the 90° phase-retarded value 231 use the same reference numeralfor convenience. V_(dc) _(—) _(qs) ^(S) represents the stator basedq-axis virtual voltage 232 and V_(dc) _(—) _(2ω) _(grid) represents thedouble system frequency component value 221 of the DC-link voltagesquare 211.

The stator based q-axis virtual voltage 232 corresponds to a valueobtained by multiplying the double system frequency component value 221of the DC-link voltage square 211 by “1”.

The fifth frame converter 240 can generate a synchronous reference framebased d-axis virtual voltage 241 and a synchronous reference frame basedq-axis virtual voltage (not shown), which are constants having a phasedifferent therebetween, using the stator based reference d-axis virtualvoltage 231, the stator reference q-axis virtual voltage 232 and thedouble system angle 251 (2θ_(g)).

The fifth frame converter 240 performs calculation according to Equation6.

$\begin{matrix}{{{R( {2\theta_{g}} )} = \begin{bmatrix}{\cos \; 2\; \theta_{g}} & {\sin \; 2\; \theta_{g}} \\{{- \sin}\; 2\; \theta_{g}} & {\cos \; 2\; \theta_{g}}\end{bmatrix}}{V_{dc\_ dqs}^{r} = {{R( {2\; \theta_{g}} )}V_{dc\_ dqs}^{s}}}} & \lbrack {{Equation}\mspace{14mu} 6} \rbrack\end{matrix}$

In Equation 6, 2θ_(g) represents the double system angle, V_(dc) _(—)_(dqs) ^(S) represents the stator based d-axis virtual voltage 231 andthe stator based q-axis virtual voltage 232, and V_(dc) _(—) _(dqs) ^(r)denotes the synchronous reference frame based d-axis virtual voltage 241and synchronous reference frame based q-axis virtual voltage.

The phase lock unit 250 can receive the synchronous reference framebased d-axis virtual voltage 241 from the fifth frame converter 240 andseparately accept a constant value “0” (243). The phase lock unit 250can generate the double system angle 251 (2θ_(g)), the double systemfrequency 252 (2ω_(grid)), the system angle 201 (θ_(g)), and the systemfrequency 202 (f_(g) or ω_(grid)).

The phase lock unit 250 may include a phase lock loop (PLL). The PLL isa frequency negative feedback circuit that locks the phase of a receivedsignal and maintains the frequency of an output signal uniform.

FIG. 5B illustrates an input waveform and calculated waveforms of thesystem angle estimator according to an embodiment of the presentinvention.

Referring to FIG. 5B, waveform a4 of the DC-link voltage 36 denoted asV_(dc) is illustrated.

In addition, waveform a5 of the double system frequency component value221 denoted as V_(dc) _(—) _(2ω) _(grid) is illustrated.

FIG. 5B also illustrates waveform a6 of the 90° phase-retarded value 231(V_(dc) _(—) _(2ω) _(grid) (θ−90°)) with respect to the double systemfrequency component value 221.

FIG. 6A illustrates a rotor based q-axis current reference generatoraccording to an embodiment of the present invention and FIG. 6Billustrates waveforms of the output torque command value and the q-axiscurrent reference value in a sine squared form according to anembodiment of the present invention.

The q-axis current reference generator 300 can respectively receive theoutput torque command value 53 and the system angle 201 from thevelocity controller (not shown) and the system angle estimator (notshown) and generate the rotor based q-axis current reference 62 in asine squared form, which is synchronized with the system angle 201.

The q-axis current reference generator 300 can generate the rotor basedq-axis current reference 62 in a sine squared form having the systemangle 201 of the power supply unit to control the power factor to be 1.

A q-axis current boundary value 417 refers to a threshold of the rotorbased q-axis current reference 62, which makes the rotor based q-axiscurrent value 42 correctly track the rotor-based q-axis currentreference value 62. That is, the q-axis current boundary value 417indicates the size of a maximum q-axis current available at the currentoperating point.

The d-axis current reference generator (not shown) can generate therotor based d-axis current reference 61 such that the rotor based q-axiscurrent reference 62 is generated within the range of the q-axis currentboundary value 417.

Accordingly, the q-axis current reference generator 300 can determinethe waveform of the rotor based reference q-axis current reference 62having an advantage in terms of power factor and harmonics.

Referring to FIGS. 6A and 6B, the q-axis current reference generator 300according to an embodiment of the present invention may include a sinesquare calculator 310, a q-axis current reference converter 320, and acurrent gain setting unit 330.

The sine square calculator 310 can receive the system angle 201 from thesystem angle estimator 200 and generate a unit sine square waveform 311having the system angle 201.

The power factor of the power supply unit (not shown) becomes 1 when therotor based q-axis current reference 62 has a sinusoidal wave formobtained when the input current and input voltage from the power supplyunit (not shown) are in-phase.

Accordingly, to determine the best form of the rotor based q-axiscurrent reference 62, output power P_(inv) of the inverter is calculatedby Equations 7 and 8.

$\begin{matrix}{P_{inv} = {1.5 \times ( {{V_{ds}^{r*}i_{ds}^{r}} + {V_{qs}^{r*}i_{qs}^{r*}}} )↵}} & \lbrack {{Equation}\mspace{14mu} 7} \rbrack \\{{P_{inv}/1.5} = {{( {{Ri}_{ds}^{r*} + {L_{d}\frac{i_{ds}^{r*}}{t}} - {\omega_{r}L_{q}i_{qs}^{r*}}} )i_{ds}^{r*}} + {( {{Ri}_{qs}^{r*} + {L_{q}\frac{i_{qs}^{r*}}{t}} + {\omega_{r}L_{d}i_{ds}^{r*}} + {\omega_{r}\lambda_{pm}}} )i_{qs}^{r*}↵}}} & \lbrack {{Equation}\mspace{14mu} 8} \rbrack\end{matrix}$

In Equations 7 and 8, V_(ds) ^(r)* denotes the rotor based d-axisvoltage reference, i_(ds) ^(r)* denotes the rotor based d-axis currentreference 61, i_(qs) ^(r)* represents the rotor based q-axis currentreference 62, V_(qs) ^(r)* represents the rotor based q-axis voltagereference, R denotes wire wound resistance of a stator, L_(d) denotesd-axis inductance, L_(q) represents q-axis inductance, ω_(r) representsrotor angular velocity, λ_(pm) represents magnetic flux of a rotor basedq-axis stator, and P_(inv) denotes output power of the inverter.

In Equations 7 and 8, when the rotor based d-axis current reference 61is controlled to be a specific value and the rotor based q-axis currentreference 62 is controlled to be sin²θ_(g) voltage

$L_{q}\frac{{di}_{qs}^{r*}}{dt}$

corresponding to a derivative term can be ignored.

Therefore, the q-axis current reference generator 300 can control thepower factor of the power supply unit to be 1 by generating the rotorbased current reference 62 in the form of sin²θ_(g).

The q-axis current reference converter 320 can receive the output torquecommand value 53 from the velocity controller (not shown) and generate aq-axis current reference 321 corresponding to the output torque commandvalue 53.

A first multiplier 340 can receive the unit sine square waveform 311from the sine square calculator 310 and accept the q-axis currentreference 321 from the q-axis current reference converter 320. The firstmultiplier 340 can generate a q-axis current reference 322 in a sinesquare form using the unit sine square waveform 311 and the q-axiscurrent reference 321.

For example, the first multiplier 340 can generate the q-axis currentreference 322 in a sine square form by multiplying the unit sine squarewaveform 311 by the q-axis current reference 321.

The current gain setting unit 330 can generate a current gain 331(K_(sc)) that makes the average of the output torque command value 53and the average a current reference modified torque 64 (T_(modi)*)generated according to the rotor based q-axis current reference 62 equalto each other.

For example, the current gain setting unit 330 can generate the currentgain 331 that makes the output torque command value 53 corresponding tothe output value of the velocity controller (not shown) equal to theaverage of torques that can be transmitted to the three-phase motor (notshown) by the inverter (not shown) that pulsates at a frequency twicethe source frequency.

A second multiplier 350 can receive the q-axis current reference 322 ina sine square form from the first multiplier 340 and accept the currentgain 331 from the current gain setting unit 330. The second multiplier350 can generate the rotor based q-axis current reference 62.

For example, the second multiplier 350 can generate the rotor basedq-axis current reference 62 by multiplying the q-axis current reference322 in a sine square form by the current gain 331.

FIG. 6B illustrates waveform a7 of the output torque command value 53and waveform a8 of a torque generated according to the q-axis currentreference 322 in a sine square form.

Periodic insufficiency of torque in a steady state, as shown in region600, can occur and the torque that is not generated periodically isaccumulated in addition to velocity pulsation due to load variation, andthus the velocity of the motor (not shown) may pulsate.

Therefore, the current gain setting unit 330 according to an embodimentof the present invention can obtain the current gain 331, which makesthe average of the output torque command value 53 corresponding to theoutput value of the velocity controller (not shown) equal to the averageof the current reference modified torque 64 generated according to therotor based q-axis current reference 62, using Equation 9.

$\begin{matrix}{{T_{modi}^{*} = {K_{sc} \times T_{sc}^{*} \times \sin^{2}\theta_{g}↵}}{{\frac{\int_{\pi}}{\omega_{grid}}T_{sc}^{*}} = {\frac{\int_{\pi}}{\omega_{grid}}T_{modi}^{*}}}{T_{sc}^{*} = {K_{sc} \times T_{sc}^{*}\frac{\int_{\pi}}{\omega_{grid}}\sin^{2}\theta_{g}\ ↵}}{T_{sc}^{*} = {\frac{K_{sc} \times T_{sc}^{*}}{2}↵}}} & \lbrack {{Equation}\mspace{14mu} 9} \rbrack\end{matrix}$

In Equation 9, T_(sc)* denotes the output torque command value 53corresponding to the output value of the velocity controller (notshown), K_(sc) denotes the current gain 331, T_(modi)* represents thecurrent reference modified torque 64 generated according to the rotorbased q-axis current reference 62, θ_(g) represents the system angle201, and ω_(grid) represents the system frequency 202.

For example, the current gain setting unit 330 can make the average ofthe output torque command value 53 corresponding to the output value ofthe velocity controller equal to the average of the current referencemodified torque 64 generated according to the rotor based q-axis currentreference 62 by setting the current gain 331 to “2”.

FIG. 7A illustrates an average voltage limit circle and load torquecurves according to an embodiment of the present invention, FIG. 7B is ablock diagram of the rotor based d-axis current reference generatoraccording to an embodiment of the present invention, and FIG. 7C is adiagram illustrating generation of the rotor based d-axis currentreference and the rotor based q-axis current reference.

Referring to FIG. 7A, an instantaneous voltage limit circle a9, anaverage voltage limit curve a10 and load torque curves a11 and a12 areshown on a d-axis and q-axis current plane.

For example, the load torque curves a11 and a12 include a motorgeneration torque curve.

In a motor driving system having a large-capacitance capacitor, theinstantaneous voltage limit circle a9 is changed only by the motorvelocity because variation in the DC-link voltage 36 can be ignored.However, when a small-capacitance capacitor is used for the DC link (notshown), the DC-link voltage 36 varies to the double system frequency 202even at a fixed velocity. Accordingly, a new “average voltage limitcircle a10” may be defined.

The instantaneous voltage limit circle a9 is a representation of avoltage limit value, which changes periodically at a specific motorvelocity, on the d-axis and q-axis current plane.

The average voltage limit curve a10 is a representation of the averageof the voltage limit value, which changes periodically at the specificmotor velocity, for a half cycle of the source frequency on the d-axisand q-axis current plane.

The average voltage limit curve a10 can be obtained by Equations 10 and11.

V _(dc) =∥V _(dc)∥sin(θ_(g))  Equation 10

In Equation 10, ∥V_(dc)∥ denotes a maximum value of the DC-link voltage36 and θ_(g) denotes the system angle 201.

$\begin{matrix}{i_{qs}^{r} = {\frac{1}{\omega_{r}L_{q}}\sqrt{\frac{V_{dc}^{2}}{3} - \{ {\omega_{r}( {\lambda_{pm} + {L_{q}i_{ds}^{r}}} )} \}^{2}}}} & \lbrack {{Equation}\mspace{14mu} 11} \rbrack\end{matrix}$

In Equation 11, i_(qs) ^(r) denotes the rotor based q-axis current,L_(d) denotes d-axis inductance, L_(q) denotes q-axis inductance, ω_(r)represents the rotor angular velocity, λ_(pm) represents magnetic fluxof the rotor based q-axis stator, i_(ds) ^(r) represents the rotor basedd-axis current, and V_(dc) ² represents the DC-link voltage square.

The rotor based q-axis current that can be obtained within the range ofthe instantaneous voltage limit value can be calculated by Equations 10and 11. The average of the rotor based q-axis current that can flow forone cycle can be obtained by averaging the rotor based q-axis currentfor one cycle.

The average voltage limit curve a10 is obtained by calculating theaverage of the rotor based q-axis current while changing the rotor basedd-axis current and representing the average on the current plane.

However, it may be necessary to consider motor parameters when theaverage voltage limit curve is generated according to Equation 11.

Accordingly, an exemplary embodiment of the present invention can use arotor based d-axis voltage boundary value 413 to obtain the correctaverage voltage limit curve without considering the motor parameters,which will be described in detail below through Equation 12.

Referring to FIG. 7A, the instantaneous voltage limit circle a9 and theaverage voltage limit curve a10 are shown on the d-axis and q-axiscurrent plane.

For example, to control a motor torque to be 2.5 [Nm], the rotor basedd-axis current reference 61 at which the average voltage limit curve a10meets a motor generated torque curve a12 needs to be maintained atapproximately −2.5 [A] and the rotor based q-axis current reference 62needs to be maintained at approximately 8 [A].

Referring to FIG. 7B, the d-axis current reference generator 400 mayinclude a current margin calculator 410, a current margin reference unit420, a first adder 430, a low pass filter 440 and a proportionalintegrator 450.

The current margin calculator 410 can generate a rotor based q-axiscurrent margin value 419. The current margin calculator 410 may includea d-axis voltage boundary value calculator 412, a unit gain calculator414, a q-axis current boundary value converter 416 and a q-axis currentmargin calculator 418.

The d-axis voltage boundary value calculator 412 can receive the rotorbased q-axis voltage limit value 102 from the third frame converter (notshown) and accept the DC-link voltage 36 from the voltage sensor (notshown). The d-axis voltage boundary value calculator 412 can generatethe rotor based d-axis voltage boundary value 413.

The d-axis voltage boundary value calculator 412 performs computationaccording to Equation 12. Here, Equation 12 is a modification ofEquation 11 and corresponds to an equation with respect to voltage.

That is, Equation 12 is obtained by modifying Equation 11 into anequation with respect to voltage.

$\begin{matrix}{{V_{ds}^{r*}{\_ boundary}} = ( \sqrt{\frac{V_{dc}^{2}}{3} - ( V_{{qs} - {sat}}^{r*} )^{2}} )} & \lbrack {{Equation}\mspace{14mu} 12} \rbrack\end{matrix}$

In Equation 12, V_(dc) ² denotes the DC-link voltage square 211,V_(qs-sat) ^(r)* denotes the rotor based q-axis voltage limit value 102,and V_(ds) ^(r)*_boundary represents the rotor based d-axis voltageboundary value 413.

The rotor based d-axis voltage boundary value 413 refers to a maximuminstantaneous voltage that can be applied to a d axis when theperiodically varying DC-link voltage 36 and the rotor based q-axisvoltage limit value 102 are taken into account.

Equation 12 uses feedback of the rotor based q-axis voltage limit valueV_(qs-sat) ^(r)*.

Since a counter electromotive force component ω_(r) (λ_(pm)+L_(d)i_(ds)^(r)) appearing at rotor based q-axis and transient voltage

$L_{q}\frac{{di}_{qs}^{r}}{dt}$

before sampling before a current reference is generated are reflected inthe rotor based q-axis voltage limit value, Equation 12 is preciser thanEquation 11 and has an advantage of requiring no motor parameters.

The unit gain calculator 414 can receive the rotor based d-axis voltagelimit value 101 from the third frame converter (not shown), receive therotor based d-axis current reference 61 from the proportional integrator450 and accept the rotor based q-axis current reference 62 from theq-axis current reference generator (not shown). The unit gain calculator414 can generate a unit gain 415 (=K_(z)=ω_(r)L_(q)).

For example, since the q-axis inductance L_(q) largely varies accordingto load condition, the unit gain 415 can be obtained using a d-axisvoltage equation (Equation 13) to design a controller robust toparameter error.

$\begin{matrix}{V_{ds}^{r} = {{R_{s}i_{ds}^{r}} + {L_{d}\frac{d}{dt}i_{ds}^{r}} - {\omega_{r}L_{q}i_{qs}^{r}}}} & \lbrack {{Equation}\mspace{14mu} 13} \rbrack\end{matrix}$

In Equation 13, V_(ds) ^(r) denotes a rotor based d-axis voltage, R_(s)denotes wire wound resistance of the stator, i_(ds) ^(r) denotes a rotorbased d-axis current, L_(d) represents d-axis inductance, ω_(r)represents the rotor angular velocity, and L_(q) represents q-axisinductance.

The q-axis current boundary value converter 416 can receive the rotorbased d-axis voltage boundary value 413 from the d-axis voltage boundaryvalue calculator 412 and accept the unit gain 415 from the unit gaincalculator 414.

The q-axis current boundary value converter 416 can generate a rotorbased q-axis boundary value 417 (i_(qs) ^(r)*−Boundary).

The rotor based q-axis current boundary value 417 refers to a maximumrotor based q-axis current that can be obtained at the current operatingpoint (velocity and load conditions).

The rotor based q-axis current boundary value 417 may be obtained on thebasis of the rotor based d-axis voltage boundary value 413 and the unitgain 415.

When the rotor based q-axis current boundary value 417 is input to a lowpass filter (not shown) located between the q-axis current boundaryvalue converter 416 and the q-axis current margin calculator 418, thelow pass filter outputs the average of the rotor based q-axis currentboundary value 417.

The average of the rotor based q-axis current boundary value 417 refersto a value obtained by averaging the rotor based q-axis current boundaryvalue 417 for one cycle of the DC-link voltage.

While FIG. 7B illustrates that the rotor based q-axis current boundaryvalue 417 is input to the q-axis current margin calculator 418 from theq-axis current boundary value converter 416, the average of the rotorbased q-axis current boundary value 417 is applied to the q-axis currentmargin calculator 418.

Therefore, an exemplary embodiment of the present invention can obtainthe average of the rotor based q-axis current boundary value 417 usingEquation 12.

The average voltage limit curve a10 is obtained by calculating theaverage of the rotor based q-axis current boundary value 417 whilechanging the rotor-based d-axis current and representing the average ofthe rotor based q-axis current boundary value 417 on the current plane.

The average of the rotor based q-axis current boundary value 417 may beused to generate the rotor based d-axis current reference value 61.

The q-axis current margin calculator 418 can receive the average of therotor based q-axis current boundary value 417 from the q-axis currentboundary value converter 416 and accept the rotor based q-axis currentreference 62 from the q-axis current reference generator 300. The q-axiscurrent margin calculator 418 can generate a rotor based q-axis currentmargin value 419.

The rotor based q-axis current margin value 419 may be obtained using adifference between the average of the rotor based q-axis currentboundary value 417 and the rotor based q-axis current reference 62.

For example, the rotor based q-axis current margin value 419 correspondsto a value obtained by subtracting the rotor based q-axis currentreference 62 from the average of the rotor based q-axis current boundaryvalue 417.

The current margin reference unit 420 can receive the output torquecommand value 53 from the velocity controller (not shown) and generate arotor based q-axis current margin reference 421.

The output torque command value 53 may refer to a value obtained bysubtracting an anti-wind up value corresponding to a torque generatedaccording to current limitation from the actually necessary torque.

Accordingly, the current margin reference unit 420 can increase therotor based-q-axis current margin reference 421 in a positive directionto compensate for insufficient torque (anti-wind up) due to currentlimitation.

For example, the current margin reference unit 420 can generate therotor based q-axis current margin reference 421 by dividing theanti-wind up value T_(e-anti) of torque output by k_(T).

When anti-windup of the torque is generated due to current limitation(e.g., generated torque is insufficient), the d-axis current referencegenerator 400 can increase rotor based q-axis current density withincurrent limitation by increasing the rotor based d-axis currentreference 61 in a negative direction.

For example, if the rotor based q-axis current reference 62 that needsto be generated is greater than the average of the rotor based q-axiscurrent boundary value 417, the current margin reference unit 420increases the rotor based q-axis current margin reference 421 in apositive direction.

As a result, the rotor based d-axis current reference 61 increases inthe negative direction and the average of the rotor based q-axis currentboundary value 417 corresponding to the increased rotor based d-axiscurrent reference 61 also increases.

The rotor based q-axis current reference value 62 corresponding to theincreased rotor based d-axis current reference 61 decreases.

On the contrary, in a steady state or when current is not limited, thecurrent margin reference unit 420 can set the rotor based q-axis currentmargin reference 421 to a value of “0”.

The rotor based d-axis current 61 is determined such that the average ofthe rotor based q-axis current boundary value 417 equals the rotor basedq-axis current reference 62.

Accordingly, the d-axis current reference generator 400 can generate thebest rotor based d-axis current reference 61 for the rotor based q-axiscurrent reference 62 in any form.

When the generated torque is insufficient due to current limitation, thed-axis current reference generator 400 can generate the rotor basedq-axis current reference 62 within the range of the q-axis currentboundary value by increasing the rotor based d-axis current reference 61in the negative direction.

Conversely, in a steady state or when current is not limited, the d-axiscurrent reference generator 400 sets the q-axis current margin reference421 to “0”. The d-axis current may be determined as a best value in asteady state regardless of the rotor based q-axis current reference 62.

The first adder 430 can receive the rotor based q-axis current marginvalue 419 and the rotor based q-axis current margin reference 421 andgenerate an error value 423 by subtracting the rotor based q-axiscurrent margin reference 421 from the rotor based q-axis current marginvalue 419.

The low pass filter 440 can obtain the average of the error value 423.While FIG. 7B illustrates only one low pass filter 440, the low passfilter can be located to obtain each of the averages of the rotor basedq-axis current reference 62, the rotor based q-axis current boundaryvalue 417 and the rotor based q-axis current margin reference value 421.

The proportional integrator 450 can receive the average of the errorvalue 423 from the first adder 430 and generate the rotor based d-axiscurrent reference 61.

When the current is limited, the current margin reference unit 420increases the rotor based q-axis current margin reference value 421 to apositive value. As a result, the average of the error value 423gradually increases, the rotor based d-axis current reference 61increases in the negative direction, and the average of the rotor basedq-axis current boundary value 417 corresponding to the increased rotorbased d-axis current reference 61 also increases.

The rotor based q-axis current reference 62 corresponding to theincreased rotor based d-axis current reference 61 decreases.

Referring to FIG. 7C, the rotor based d-axis current reference and therotor based q-axis current reference can be generated in a dashed area.

That is, the rotor based d-axis current reference can be generated inthe range of 0 to P0 (e.g.,

$ \lbrack { 0 \sim{- \frac{\lambda_{pm}}{L_{d}}}} \rbrack ).$

The velocity controller (not shown) generates the output torque commandvalue 53 such that the steady state can be maintained.

The current reference generator (not shown) can generate an instructioncorresponding to point P1 (at which the rotor based q-axis currentreference=8.5 [A] and the rotor based d-axis current reference=0 [A]) togenerate a load torque curve a12 of 2.5 [Nm].

However, the rotor based q-axis current cannot be 8.5 [A] when thevoltage corresponding to an instantaneous voltage limit circle (a curvelocated in the range of 220 [V] to 250 [V] of a9) is applied.

This is because the rotor based q-axis current that can be actuallygenerated is 7.0 [A] although the rotor based q-axis current referenceis 8.5 [A].

In this case, the generated torque becomes lower than a load torque soas to decrease the motor velocity.

To compensate for the motor velocity decrease, the current marginreference unit 420 can generate the rotor based q-axis current marginreference value 421.

For example, the current margin reference unit 420 can generate therotor based q-axis current margin reference value 421 of 1.0 [A] toincrease the generated torque (to generate 9.5 [A] greater than 8.5[A]).

Generation of the rotor based q-axis current margin reference value 421by the current margin reference unit 420 can be regarded as confirmationof a current margin for the torque. That is, the average of the rotorbased q-axis current boundary value needs to increase by 1 [A].

The current margin calculator 410 checks an instantaneous state in whichthe DC-link voltage pulsates.

When the rotor based d-axis current reference 61 is 0 [A], the rotorbased q-axis current boundary value 417 can continuously vary in therange of 0 to 15 [A] according to a pulsating voltage.

The average of the rotor based q-axis current boundary value 417 has avalue of 7.0 [A] (P3). This value represents the threshold of the rotorbased q-axis current that can be actually generated.

Accordingly, even if the q-axis current reference generator 300generates the rotor based q-axis current reference 62 corresponding to8.5 [A], the actually generated rotor-based q-axis current is merely 7.0[A] (P3).

The q-axis current margin calculator 418 generates −1.5 [A]corresponding to the difference between the average of the rotor basedq-axis current boundary value 417, 7.0 [A], and the rotor based q-axiscurrent reference, 8.5 [A]. That is, the rotor based q-axis currentmargin value 419 is −1.5 [A].

When an error value between the rotor based q-axis current marginreference 421 and the rotor based q-axis current margin value 419 passesthrough the low pass filter 440 and the proportional integrator 450, therotor based d-axis current reference corresponding to a negative valueis generated.

By repeating this procedure, the rotor based current reference 62converges on point P2 from point P1 and the average of the rotor basedq-axis current boundary value 417 converges on P2 from P3.

That is, the rotor based q-axis current reference 62 gradually decreasesto converge on P2 because the rotor based d-axis current reference 61makes up for the insufficient torque.

FIG. 8 is a flowchart illustrating a method to control an invertercontrol apparatus according to an embodiment of the present invention.

In the method to control the inverter control apparatus 1 that drives athree-phase motor and controls an inverter having a DC-link voltage thatpulsates at a frequency twice a system frequency according to anembodiment of the present invention, the inverter control apparatus 1includes a current sensor, a voltage sensor and a controller. In theinverter control apparatus 1, the controller receives an inverter outputcurrent value from the current sensor and accepts an inverter DC-linkvoltage value from the voltage sensor to estimate a system angle or asystem frequency. The controller generates a rotor based q-axis currentreference in a sine squared form, which is synchronized with the systemangle, averages a periodically varying voltage limit value for a halfcycle of the system frequency to generate the average rotor based q-axiscurrent value, and generates a rotor based d-axis current reference onthe basis of the average rotor based q-axis current value.

The inverter control apparatus 1 may receive an output phase currentsense signal of the inverter 5, which is an analog signal, from thecurrent sensor 6 and receives a voltage sense signal of the DL link 4,which is an analog signal, from the voltage sensor 7 (1000).

The inverter control apparatus 1 can estimate the position of a rotorwithout using a position sensor. That is, the inverter control apparatus1 can generate the rotor angular position estimate 11 (θ_(r)). Theinverter control apparatus 1 can generate the rotor angular velocityestimate 21 (ω_(r)) by differentiating the rotor angular positionestimate 11 (1100).

The inverter control apparatus 1 can receive the output phase currentsense signal of the inverter 5, which is an analog signal, from thecurrent sensor 6 and generate the three-phase motor input phase currentvalues 32, 33 and 34 corresponding to digital signals.

The inverter control apparatus 1 can receive the voltage sense signal ofthe DC link 4, which corresponds to an analog signal, from the voltagesensor 7 and generate a DC-link voltage 36 corresponding to a digitalsignal.

The inverter control apparatus 1 frame-converts the three-phase motorinput phase current values 32, 33 and 34 to rotor based two-phasecurrent 41 and 42.

The first frame converter 40 receives the three-phase motor input phasecurrent values 32, 33 and 34 from the current sensor 6 and receives therotor angular position estimate 11 from the rotor angular positionestimator 10.

The inverter control apparatus 1 can generate the rotor based d-axiscurrent value 41 and the rotor based q-axis current value 42, which areconstants having a phase difference of 90° therebetween using thethree-phase motor input phase current values 32, 33 and 34 and the rotorangular position estimate 11.

The inverter control apparatus 1 can generate the output torque commandvalue 53 using the rotor angular velocity reference 51 and the rotorangular velocity estimate 21 (1200).

The inverter control apparatus 1 can generate the rotor based d-axiscurrent reference 61 and the rotor based q-axis current reference 62using the output torque command value 53, the rotor based d-axis voltagelimit value 101, the rotor based q-axis voltage limit value 102 and theDC-link voltage 36 (1300).

Generation of the rotor based d-axis current reference 61 and the rotorbased q-axis current reference 62 by the inverter control apparatus 1has been described with reference to FIG. 4.

The inverter control apparatus 1 can generate the rotor based d-axisvoltage reference 71 and the rotor based q-axis voltage reference 72using the rotor based d-axis current reference 61, the rotor basedq-axis current reference 62, the rotor based d-axis current value 41 andthe rotor based q-axis current value 42 (1400).

The inverter control apparatus 1 can generate the stator based d-axisvoltage reference 81 and the stator based q-axis voltage reference 82,which are AC values having a phase difference of 90° therebetween, usingthe rotor based d-axis voltage reference 71, the rotor based q-axisvoltage reference 72 and the rotor angular position estimate 11 (1500).

The inverter control apparatus 1 can generate the stator based d-axisvoltage limit value 91 and a stator based q-axis voltage limit value 92using the stator based d-axis voltage reference 81, the stator basedq-axis voltage reference 82 and the DC-link voltage 36 (1600).

The inverter control apparatus 1 can generate the rotor based d-axisvoltage limit value 101 and the rotor based q-axis voltage limit value102, which have a phase difference of 90° therebetween, using the statorbased d-axis voltage limit value 91, the stator based q-axis voltagelimit value 92 and the rotor angular position estimate 11.

The inverter control apparatus 1 can generate the three-phase voltagereferences 111, 112 and 113 which are three-phase AC values using thestator based d-axis voltage limit value 91 and the stator based q-axisvoltage limit value 92 (1700).

The inverter control apparatus 1 can generate the switching controlsignals 121 to 126 of the 6 switches (not shown) of the inverter (notshown) using the three-phase voltage references 111, 112 and 113 androtor angular position estimate 11 (1800).

FIG. 9 illustrates a method to generate rotor based d-axis and q-axiscurrent references according to an embodiment of the present invention.

The inverter control apparatus 1 according to an embodiment of thepresent invention can take an error in motor parameters of the motorvoltage equation into account even if the inverter control apparatus 1is not aware of the motor parameters and provide a high-reliabilitycontrol method through system angle estimation.

Referring to FIG. 9, the inverter control apparatus 1 can generate thesystem angle 201, the system frequency 202, the double system angle 251and the double system frequency 252 using the DC-link voltage 36 (1310).

The inverter control apparatus 1 can generate the rotor based q-axiscurrent reference 62 in a sine squared form, which is synchronized withthe system angle, using the output torque command value 53 and thesystem angle 201 (1320).

The inverter control apparatus 1 can generate the rotor based d-axiscurrent reference 61 using the output torque command value 53, theDC-link voltage 36, the rotor based q-axis current reference 62, therotor based d-axis voltage limit value 101, the rotor based q-axisvoltage limit value 102, and the rotor based d-axis current reference 61received through feedback (1330).

FIG. 10 illustrates a method to estimate a system angle according to anembodiment of the present invention.

The inverter control apparatus 1 can generate the DC-link voltage square211 using the DC-link voltage 36 (1312).

The DC-link voltage square 211 is obtained by squaring the DC-linkvoltage 36.

The inverter control apparatus 1 can generate the double systemfrequency component value 221 (V_(dc) _(—) _(2ω) _(grid) ) of theDC-link voltage square 211 using the DC-link voltage square 211 and thedouble system frequency 252 (2ω_(grid)) (1314).

For example, the inverter control apparatus 1 can set the frequencytwice the system frequency (50 Hz or 60 Hz) to an initial value, and usethe double system frequency 252 (2ω_(grid)) by feeding back the same incases other than a case in which the motor is driven.

The inverter control apparatus 1 can perform calculations according toEquation 3.

V _(dc) _(—) _(2ω) _(grid) =BPF(V _(dc) ²,2ω_(grid))  Equation 3

In Equation 3, V_(dc) ² denotes the DC-link voltage square, ω_(grid)denotes the system frequency, and V_(dc) _(—) _(2ω) _(grid) representsthe double system frequency component value 221 of the DC-link voltagesquare 211.

The inverter control apparatus 1 can generate the 90° phase-retardedvalue 231 (V_(dc) _(—) _(2ω) _(grid) (θ−90°)) having a phase retarded by90° from the double system frequency component value 221 using thedouble system frequency component value 221 of the DC-link voltagesquare 211 (1316).

The inverter control apparatus 1 can perform calculations according toEquation 4.

V _(dc) _(—) _(2ω) _(grid) (θ−90°)=SOGI(V _(dc) _(—) _(2ω) _(grid) )

or V _(dc) _(—) _(2ω) _(grid) (θ−90°)=APF(V _(dc) _(—) _(2ω) _(grid))  Equation 4

In Equation 4, V_(dc) _(—) _(2ω) _(grid) denotes the double systemfrequency component value 221 of the DC-link voltage square 211, SOGI(Second Order General Integrator) denotes a secondary generalintegrator, APF represents an all-pass filter, and V_(dc) _(—) _(2ω)_(grid) (θ−90°) represents the 90° phase-retarded value 231.

For example, the inverter control apparatus 1 can include an all-passfilter or a secondary general integrator.

The inverter control apparatus 1 can perform frame conversion (1317).

That is, the inverter control apparatus 1 can generate the synchronousreference frame based d-axis virtual voltage 241 and the synchronousreference frame based q-axis virtual voltage (not shown), which areconstants having a phase difference therebetween, using the stator basedd-axis virtual voltage 231, the stator based q-axis virtual voltage 232,and the double system angle 251.

The stator based d-axis virtual voltage 231 (V_(dc) _(—) _(ds) ^(S)) andthe stator based q-axis virtual voltage 232 (V_(dc) _(—) _(qs) ^(S)) canbe defined by Equation 5.

V _(dc) _(—) _(ds) ^(S) =V _(dc) _(—) _(2ω) _(grid) (θ−90°)

V _(dc) _(—) _(qs) ^(S) =−V _(dc) _(—) _(2ω) _(grid)   Equation 5

In Equation 5, V_(dc) _(—) _(ds) ^(S) denotes the stator based d-axisvirtual voltage 231 and V_(dc) _(—) _(2ω) _(grid) (θ−90°) denotes the90° phase-retarded value 231. The stator based d-axis virtual voltage231 and the 90° phase-retarded value 231 use the same reference numeralfor convenience. V_(dc) _(—) _(qs) ^(S) represents the stator basedq-axis virtual voltage 232 and V_(dc) _(—) _(2ω) _(grid) represents thedouble system frequency component value 221 of the DC-link voltagesquare 211.

The stator based q-axis virtual voltage 232 corresponds to a valueobtained by multiplying the double system frequency component value 221of the DC-link voltage square 211 by “1”.

The inverter control apparatus 1 can generate the synchronous referenceframe based d-axis virtual voltage 241 and the synchronous referenceframe based q-axis virtual voltage (not shown), which are constantshaving a phase difference therebetween, using the stator based d-axisvirtual voltage 231, the stator based q-axis virtual voltage 232, andthe double system angle 251 (2θ_(g)).

The inverter control apparatus 1 performs calculation according toEquation 6.

$\begin{matrix}{{{R( {2\theta_{g}} )} = \begin{bmatrix}{\cos \; 2\; \theta_{g}} & {\sin \; 2\; \theta_{g}} \\{{- \sin}\; 2\; \theta_{g}} & {\cos \; 2\; \theta_{g}}\end{bmatrix}}{V_{dc\_ dqs}^{r} = {{R( {2\theta_{g}} )}V_{dc\_ dqs}^{s}}}} & \lbrack {{Equation}\mspace{14mu} 6} \rbrack\end{matrix}$

In Equation 6, 2θ_(g) represents the double system angle, V_(dc) _(—)_(dqs) ^(S) represents the stator based d-axis virtual voltage 231 andthe stator based q-axis virtual voltage 232, and V_(dc) _(—) _(dqs) ^(r)denotes the synchronous reference frame based d-axis virtual voltage 241and synchronous reference frame based q-axis virtual voltage 242.

The inverter control apparatus 1 can generate the double system angle251 (2θ_(g)), the double system frequency 252 (2ω_(grid)), the systemangle 201 (θ_(g)), and the system frequency 202 (f_(g) or ω_(grid))using the synchronous reference frame based d-axis virtual voltage 241and the constant “0” (243) (1318).

The inverter control apparatus 1 may include a phase lock loop (PLL).The PLL is a frequency negative feedback circuit that locks the phase ofa received signal and maintains the frequency of an output signaluniform.

FIG. 11 illustrates a method to generate a q-axis current referenceaccording to an embodiment of the present invention.

The inverter control apparatus 1 can generate the rotor based q-axiscurrent reference 62 in a sine squared form having the system angle 201of the power supply unit to control the power factor to be 1.

A q-axis current boundary value refers to a threshold of the rotor basedq-axis current reference 62, which makes the rotor based q-axis currentvalue correctly track the rotor-based q-axis current reference value.

The inverter control apparatus 1 can generate the rotor based d-axiscurrent reference such that the rotor based q-axis current reference 62is generated within the range of the q-axis current boundary value 417.

Accordingly, the inverter control apparatus 1 can determine the waveformof the rotor based reference q-axis current reference 62 having anadvantage in terms of power factor and harmonics.

The inverter control apparatus 1 can generate the unit sine squarewaveform 311 having the system angle 201 using the system angle 201.

The power factor of the power supply unit (not shown) becomes 1 when therotor based q-axis current reference 62 has a sinusoidal wave formobtained when the input current and input voltage from the power supplyunit (not shown) are in-phase.

Accordingly, to determine the best form of the rotor based q-axiscurrent reference 62, output power P_(inv) of the inverter is calculatedby Equations 7 and 8.

$\begin{matrix}{P_{inv} = {1.5 \times ( {{V_{ds}^{r*}i_{ds}^{r}} + {V_{qs}^{r*}i_{qs}^{r*}}} )_{↵}}} & \lbrack {{Equation}\mspace{14mu} 7} \rbrack \\{{{P_{inv}/1.5} = {{( {{Ri}_{ds}^{r*} + {L_{d}\frac{{di}_{ds}^{r*}}{dt}} - {\omega_{r}L_{q}i_{qs}^{r*}}} )i_{ds}^{r*}} + {( {{Ri}_{qs}^{r*} + {L_{q}\frac{{di}_{qs}^{r*}}{dt}} + {\omega_{r}L_{d}i_{ds}^{r*}} + {\omega_{r}\lambda_{pm}}} )i_{qs}^{r*}}}},} & \lbrack {{Equation}\mspace{14mu} 8} \rbrack\end{matrix}$

In Equations 7 and 8, V_(ds) ^(r)* denotes the rotor based d-axisvoltage reference, denotes the rotor based d-axis current reference 61,i_(qs) ^(r)* represents the rotor based q-axis current reference 62,V_(qs) ^(r)* represents the rotor based q-axis voltage reference, Rdenotes wire wound resistance of a stator, L_(d) denotes d-axisinductance, L_(q) represents q-axis inductance, ω_(r) represents rotorangular velocity, λ_(pm) represents magnetic flux of a rotor basedq-axis stator, and P_(inv) denotes output power of the inverter.

In Equations 7 and 8, when the rotor based d-axis current reference 61is controlled to be a specific value and the rotor based q-axis currentreference 62 is controlled to be sin²θ_(g), voltage

$L_{q}\frac{{di}_{qs}^{r*}}{dt}$

corresponding to a derivative term can be ignored.

Therefore, the inverter control apparatus 1 can control the power factorof the power supply unit to be 1 by generating the rotor based currentreference 62 in the form of sin²θ_(g) (1322).

The inverter control apparatus 1 can generate the q-axis currentreference 321 corresponding to the output torque command value 53 usingthe output torque command value 53 (1324).

The inverter control apparatus 1 can generate the q-axis currentreference 322 in a sine square form using the unit sine square waveform311 and the q-axis current reference 321.

For example, the inverter control apparatus 1 can generate the q-axiscurrent reference 322 in a sine square form by multiplying the unit sinesquare waveform 311 by the q-axis current reference 321 (1326).

The inverter control apparatus 1 can generate the current gain 331(K_(sc)) that makes the average of the output torque command value 53and the average a current reference modified torque 64 (T_(modi)*)generated according to the rotor based q-axis current reference 62 equalto each other.

For example, the inverter control apparatus 1 can generate the currentgain 331 that makes the output torque command value 53 equal to theaverage of torques that can be transmitted to the three-phase motor (notshown) by the inverter (not shown) that pulsates at a frequency twicethe source frequency.

The inverter control apparatus 1 can generate the rotor based q-axiscurrent reference 62 using the q-axis current reference 322 and thecurrent gain 331.

For example, the inverter control apparatus 1 can generate the rotorbased q-axis current reference 62 by multiplying the q-axis currentreference 322 in a sine square form by the current gain 331 (1328).

FIG. 6B illustrates a waveform a7 of the output torque command value 53and waveform a8 of a torque generated according to the q-axis currentreference 322 in a sine square form.

In this case, periodic insufficiency of torque in a steady state, asillustrated in region A, can occur and the torque that is not generatedperiodically is accumulated in addition to velocity pulsation due toload variation, and thus the velocity of the motor (not shown) maypulsate.

Therefore, the inverter control apparatus 1 according to an embodimentof the present invention can obtain the current gain 331, which makesthe average of the output torque command value 53 equal to the averageof the current reference modified torque 64 generated according to therotor based q-axis current reference 62, using Equation 9.

$\begin{matrix}{{T_{modi}^{*} = {K_{sc} \times T_{sc}^{*} \times \sin^{2}\theta_{g}↵}}{{\frac{\int_{\pi}}{\omega_{grid}}T_{sc}^{*}} = {\frac{\int_{\pi}}{\omega_{grid}}T_{modi}^{*}}}{T_{sc}^{*} = {K_{sc} \times T_{sc}^{*}\frac{\int_{\pi}}{\omega_{grid}}\sin^{2}\theta_{g}\ ↵}}{T_{sc}^{*} = {\frac{K_{sc} \times T_{sc}^{*}}{2}↵}}} & \lbrack {{Equation}\mspace{14mu} 9} \rbrack\end{matrix}$

In Equation 9, T_(sc)* denotes the output torque command value 53,K_(sc) denotes the current gain 331, T_(modi)* represents the currentreference modified torque 64 generated according to the rotor basedq-axis current reference 62, θ_(g) represents the system angle 201, andω_(grid) represents the system frequency 202.

For example, the inverter control apparatus 1 can make the average ofthe output torque command value 53 corresponding to the output value ofthe velocity controller equal to the average of the current referencemodified torque 64 generated according to the rotor based q-axis currentreference 62 by setting the current gain 331 to “2”.

FIG. 12 is a flowchart illustrating a method to generate a d-axiscurrent reference according to an embodiment of the present invention.

Referring to FIG. 7A, the instantaneous voltage limit circle a9, theaverage voltage limit curve a10 and load torque curves a11 and a12 areillustrated on a d-axis and q-axis current plane.

In a motor driving system having a large-capacitance capacitor, theinstantaneous voltage limit circle a9 is changed only by the motorvelocity because variation in the DC-link voltage 36 can be ignored.However, when a small-capacitance capacitor may be used for the DC link(not shown), the DC-link voltage 36 varies to the double systemfrequency 202 even at a fixed velocity. Accordingly, a new “averagevoltage limit circle a10” is defined.

The instantaneous voltage limit circle a9 is a representation of avoltage limit value, which changes periodically at a specific motorvelocity, on the d-axis and q-axis current plane.

The average voltage limit curve a10 is a representation of the averageof the voltage limit value, which changes periodically at the specificmotor velocity, for a half cycle of the source frequency on the d-axisand q-axis current plane.

The average voltage limit curve a10 can be obtained by Equations 10 and11.

V _(dc) =∥V _(dc)∥sin(θ_(g))  Equation 10

In Equation 10, ∥V_(dc)∥ is denotes a maximum value of the DC-linkvoltage 36 and θ_(g) denotes the system angle 201.

$\begin{matrix}{i_{qs}^{r} = {\frac{1}{\omega_{r}L_{q}}\sqrt{\frac{V_{dc}^{2}}{3} - \{ {\omega_{r}( {\lambda_{pm} + {L_{d}i_{ds}^{r}}} )} \}^{2}}}} & \lbrack {{Equation}\mspace{14mu} 11} \rbrack\end{matrix}$

In Equation 11, i_(qs) ^(r) denotes the rotor based q-axis current,L_(d) denotes d-axis inductance, L_(q) denotes q-axis inductance, ω_(r)represents the rotor angular velocity, λ_(pm) represents magnetic fluxof the rotor based q-axis stator, i_(ds) ^(r) represents the rotor basedd-axis current, and V_(dc) ² represents the DC-link voltage square.

The rotor based q-axis current that can be obtained within the range ofthe instantaneous voltage limit value can be calculated by Equations 10and 11. The average of the rotor based q-axis current that can flow forone cycle can be obtained by averaging the rotor based q-axis currentfor one cycle.

The average voltage limit curve a10 is obtained by calculating theaverage of the rotor based q-axis current while changing the rotor basedd-axis current and representing the average on the current plane.

However, it is necessary to consider motor parameters when the averagevoltage limit curve is generated according to Equation 11.

Accordingly, the present invention can use a rotor based d-axis voltageboundary value 413 to obtain the correct average voltage limit curvewithout considering the motor parameters, which will be described indetail below through Equation 12.

Referring to FIG. 7A, the instantaneous voltage limit circle a9 and theaverage voltage limit curve a10 are illustrated on the d-axis and q-axiscurrent plane.

For example, to control a motor torque to be 2.5 [Nm], the rotor basedd-axis current reference 61 at which the average voltage limit curve a10meets a motor generated torque curve a12 needs to be maintained atapproximately −2.5 [A] and the rotor based q-axis current reference 62needs to be maintained at approximately 8 [A].

Referring to FIG. 12, the inverter control apparatus 1 can generate therotor based d-axis voltage boundary value 413 using the rotor basedq-axis voltage limit value 102 and the DC-link voltage 36.

The inverter control apparatus 1 performs computation according toEquation 12. Here, Equation 12 is a modification of Equation 11 andcorresponds to an equation with respect to voltage.

That is, Equation 12 is obtained by modifying Equation 11 into anequation with respect to voltage.

$\begin{matrix}{{V_{ds}^{r*}{\_ boundary}} = ( \sqrt{\frac{V_{dc}^{2}}{3} - ( V_{{qs} - {sat}}^{r*} )^{2}} )} & \lbrack {{Equation}\mspace{14mu} 12} \rbrack\end{matrix}$

In Equation 12, V_(dc) ² denotes the DC-link voltage square 211,V_(qs-sat) ^(r)* denotes the rotor based q-axis voltage limit value 102,and V_(ds) ^(r)*_boundary represents the rotor based d-axis voltageboundary value 413.

The rotor based d-axis voltage boundary value 413 refers to a maximuminstantaneous voltage that can be applied to a d axis when theperiodically varying DC-link voltage 36 and the rotor based q-axisvoltage limit value 102 are taken into account.

Equation 12 uses feedback of the rotor based q-axis voltage limit valueV_(qs-sat) ^(r)*.

Since a counter electromotive force component ω_(r)(λ_(pm)+L_(d)i_(ds)^(r)) appearing at rotor based q-axis and transient voltage

$L_{q}\frac{{di}_{qs}^{r}}{dt}$

before sampling before a current reference is generated are reflected inthe rotor based q-axis voltage limit value, Equation 12 is preciser thanEquation 11 and has an advantage of requiring no motor parameters(1331).

The inverter control apparatus 1 can generate a unit gain 415(=K₂=ω_(r)L_(q)) using the rotor based d-axis voltage limit value 101,the rotor based d-axis current reference 61 and the rotor based q-axiscurrent reference 62.

For example, since the q-axis inductance L_(q) largely varies accordingto load condition, the unit gain 415 can be obtained using a d-axisvoltage equation (Equation 13) to design a controller robust toparameter error.

$\begin{matrix}{V_{ds}^{r} = {{R_{s}i_{ds}^{r}} + {L_{d}\frac{d}{dt}i_{ds}^{r}} - {\omega_{r}L_{q}i_{qs}^{r}}}} & \lbrack {{Equation}\mspace{14mu} 13} \rbrack\end{matrix}$

In Equation 13, V_(ds) ^(r) denotes a rotor based d-axis voltage, R_(s)denotes wire wound resistance of the stator, i_(ds) ^(r) denotes a rotorbased d-axis current, L_(d) represents d-axis inductance, ω_(r)represents the rotor angular velocity, and L_(q) represents q-axisinductance (1332).

The inverter control apparatus 1 c can generate the rotor based q-axisboundary value 417 (i_(qs) ^(r)*−Boundary) using the rotor based d-axisvoltage boundary value 413 and the unit gain 415.

The rotor based q-axis current boundary value 417 refers to a maximumrotor based q-axis current that can be obtained at the current operatingpoint (velocity and load conditions). The rotor based q-axis currentboundary value 417 is obtained on the basis of the rotor based d-axisvoltage boundary value 413 and the unit gain 415.

The average of the rotor based q-axis current boundary value 417 may beused to generate the rotor based d-axis current reference 61.

That is, the average of q-axis current that can flow during one cyclecan be obtained by averaging the rotor based q-axis current boundaryvalue 417 for one cycle of the DC-link voltage. The average voltagelimit curve a10 is obtained by calculating the average of the rotorbased q-axis current boundary value 417 while changing the rotor-basedd-axis current and representing the average of the rotor based q-axiscurrent boundary value 417 on the current plane.

For example, if the average of the rotor based q-axis current reference62 that needs to be generated is greater than the average of the rotorbased q-axis current boundary value 417, the inverter control apparatus1 can increase the average of the rotor based q-axis current boundaryvalue 417 by setting the rotor based d-axis current reference 61 to anegative value (1333).

The inverter control apparatus 1 can generate the rotor based q-axiscurrent margin value 419 using the rotor based q-axis current boundaryvalue 417 and the rotor based q-axis current reference 62. The rotorbased q-axis current margin value 419 is obtained using a differencebetween the average of the rotor based q-axis current boundary value 417and the rotor based q-axis current reference 62 (1334).

The inverter control apparatus 1 can generate the rotor based q-axiscurrent margin reference 421 isomg the output torque command value 53.

The output torque command value 53 may refer to a value obtained bysubtracting an anti-wind up value corresponding to a torque generatedaccording to current limitation from the actually necessary torque.

Accordingly, the inverter control apparatus 1 can increase the rotorbased-q-axis current margin reference 421 in a positive direction tocompensate for insufficient torque (anti-wind up) due to currentlimitation.

For example, the inverter control apparatus 1 can generate the rotorbased q-axis current margin reference 421 by dividing the anti-wind upvalue T_(e-anti) of torque output by k_(T).

When anti-windup of the torque is generated due to current limitation(e.g., generated torque is insufficient), the inverter control apparatus1 can increase rotor based q-axis current density within currentlimitation by increasing the rotor based d-axis current reference 61 ina negative direction.

For example, if the rotor based q-axis current reference 62 that needsto be generated is greater than the average of the rotor based q-axiscurrent boundary value 417, the inverter control apparatus 1 increasesthe rotor based q-axis current margin reference 421 in a positivedirection.

As a result, the rotor based d-axis current reference 61 increases inthe negative direction and the average of the rotor based q-axis currentboundary value 417 corresponding to the increased rotor based d-axiscurrent reference 61 also increases.

The rotor based q-axis current reference value 62 corresponding to theincreased rotor based d-axis current reference 61 decreases.

On the contrary, in a steady state or when current is not limited, theinverter control apparatus 1 can set the rotor based q-axis currentmargin reference 421 to “0”.

In this case, the rotor based d-axis current 61 may be determined suchthat the average of the rotor based q-axis current boundary value 417equals the rotor based q-axis current reference 62.

Accordingly, the inverter control apparatus 1 can generate the bestrotor based d-axis current reference 61 for the rotor based q-axiscurrent reference 62 in any form.

When the generated torque is insufficient due to current limitation, theinverter control apparatus 1 can generate the rotor based q-axis currentreference 62 within the range of the q-axis current boundary value byincreasing the rotor based d-axis current reference 61 in the negativedirection.

Conversely, in a steady state or when current is not limited, theinverter control apparatus 1 sets the q-axis current margin reference421 to “0”. In this case, the d-axis current is determined as a bestvalue in a steady state regardless of the rotor based q-axis currentreference 62.

The inverter control apparatus 1 can generate the error value 423 bysubtracting the rotor based q-axis current margin reference 421 from therotor based q-axis current margin value 419 using the rotor based q-axiscurrent margin value 419 and the rotor based q-axis current marginreference 421.

The inverter control apparatus 1 can sequentially input the error value423 to a low pass filter and a proportional integrator to generate therotor based d-axis current reference 61 (1336).

FIG. 13 illustrates motor driving waveforms when a compressor of a 1 kWair-conditioner is controlled at 5400 r/min according to an embodimentof the present invention.

FIG. 13 illustrates a waveform a13 of the rotor based q-axis currentreference, waveform a14 of a rotor based q-axis current measurementvalue, waveform a16 of the rotor based d-axis current reference, andwaveform a17 of a rotor based d-axis current measurement value.

Referring to FIG. 13, when a load torque is increased, both the rotorbased q-axis current reference and the rotor based q-axis currentmeasurement value increase (a15).

When the load torque is increased, the rotor based reference d-axiscurrent reference generated through average voltage limitation increasesin a negative direction (a18) to secure a voltage margin for theincreasing rotor based q-axis current.

FIG. 14 illustrates waveforms of the current and voltage of input poweraccording to an embodiment of the present invention.

Referring to FIG. 14, a current waveform a19 and voltage waveform a20 ofthe input power are illustrated.

When harmonics and power factor of the input current are calculated inthe case of a normal load torque size, the power factor is 97.3%. Thisis because q-axis current is synchronized with system voltage to bemodified into sin²θ_(g).

FIG. 15 illustrates an input current harmonics analysis result accordingto an embodiment of the present invention.

Referring to FIG. 15, input current harmonics a21 satisfy criteria a22of IEC 61000-3-2 Class A.

Although a few embodiments of the present invention have been shown anddescribed, it would be appreciated by those skilled in the art thatchanges may be made in these embodiments without departing from theprinciples and spirit of the invention, the scope of which is defined inthe claims and their equivalents.

What is claimed is:
 1. An inverter control apparatus that controls aninverter having a DC-link voltage pulsating at double a systemfrequency, the inverter control apparatus comprising: a current sensorto sense an output current of the inverter; a voltage sensor to sense aDC-link voltage of the inverter; and a controller to generate an averageof a periodically varying rotor based q-axis current boundary value on abasis of the output current and the DC-link voltage, to generate acurrent reference on a basis of the average of the rotor based q-axiscurrent boundary value, and to drive a three-phase motor on the basis ofthe current reference.
 2. The inverter control apparatus according toclaim 1, wherein the controller comprises: a velocity controller togenerate an output torque command value on the basis of the outputcurrent; and a current reference generator to generate the currentreference corresponding to the output torque command value.
 3. Theinverter control apparatus according to claim 2, wherein the currentreference generator comprises a system angle estimator to estimate atleast one of a system angle, a system frequency, a double system angleand a double system frequency on the basis of the DC-link voltage. 4.The inverter control apparatus according to claim 3, wherein the currentreference generator further comprises a q-axis current referencegenerator to generate a rotor based q-axis current reference in a sinesquared form, which is synchronized with the system angle, on the basisof the system angle.
 5. The inverter control apparatus according toclaim 4, wherein the current reference generator further comprises ad-axis current reference generator to calculate the average of theperiodically varying rotor based q-axis current boundary value and togenerate a rotor based d-axis current reference on the basis of theaverage of the rotor based q-axis current boundary value and the rotorbased q-axis current reference.
 6. The inverter control apparatusaccording to claim 3, wherein the system angle estimator comprises: aDC-link voltage square calculator to square the DC-link voltage togenerate a DC-link voltage square; a band pass filter to generate adouble system frequency component value having a frequency twice thesystem frequency on the basis of the DC-link voltage square and thedouble system frequency; a phase retarder to generate a 90°phase-retarded value having a phase retarded by 90° from the doublesystem frequency component value; a fifth frame converter to generate asynchronous reference frame based d-axis virtual voltage and asynchronous reference frame based q-axis virtual voltage, which areconstants and have a phase difference therebetween, on the basis of the90°-phase-retarded value, a value obtained by multiplying the doublesystem frequency component value by “−1”, and the double system angle;and a phase lock unit to generate at least one of the system angle, thesystem frequency, the double system angle, and the double systemfrequency on the synchronous reference frame based d-axis virtualvoltage and constant “0”.
 7. The inverter control apparatus according toclaim 6, wherein the phase lock unit comprises an all-pass filter or asecondary general integrator to retard a phase.
 8. The inverter controlapparatus according to claim 6, wherein the phase lock unit comprises aphase lock loop to lock the phase of a received signal and keep thefrequency of an output signal uniform.
 9. The inverter control apparatusaccording to claim 4, wherein the q-axis current reference generatorcomprises: a sine square calculator to generate a unit sine squarewaveform having the system angle; a q-axis current reference converterto generate a q-axis current reference corresponding to the outputtorque command value; a first multiplier to multiply the unit sinesquare waveform by the q-axis current reference to generate a q-axiscurrent reference in a sine squared form; a current gain setting unit togenerate a current gain that makes the average of the output torquecommand value equal to the average of a current reference modifiedtorque generated according to the rotor based q-axis current reference;and a second multiplier to multiply the q-axis current reference in asine squared form by the current gain to generate a rotor based q-axiscurrent reference.
 10. The inverter control apparatus according to claim9, wherein the current gain setting unit sets the current gain to “2”.11. The inverter control apparatus according to claim 5, wherein thed-axis current reference generator comprises: a current margincalculator to calculate the average of the periodically varying rotorbased q-axis current boundary value on the basis of the DC-link voltageand to generate a rotor based q-axis current margin value on the basisof the average of the rotor based q-axis current boundary value; acurrent margin reference unit to generate a rotor based q-axis currentmargin reference on the basis of the output torque command value; and afirst adder to generate an error value by subtracting the rotor basedq-axis current margin reference from the rotor based q-axis currentmargin value.
 12. The inverter control apparatus according to claim 11,wherein the current margin calculator comprises: a d-axis voltageboundary value calculator to generate a rotor based d-axis voltageboundary value corresponding to a maximum instantaneous voltage that canbe applied to a d axis on the basis of the DC-link voltage; a unit gaincalculator to generate a unit gain that changes a voltage value into acurrent value; a q-axis current boundary converter to generate a rotorbased q-axis current boundary value on the basis of the rotor basedd-axis voltage boundary value and the unit gain; and a q-axis currentmargin calculator to subtract the rotor based q-axis current referencefrom the average of the rotor based q-axis current boundary value togenerate a rotor based q-axis margin value.
 13. The inverter controlapparatus according to claim 11, wherein the current margin referenceunit sets the rotor based d-axis current reference to a positive valuesuch that the rotor based d-axis current reference is set to a negativevalue when a generated torque is insufficient due to current limitation.14. The inverter control apparatus according to claim 11, wherein thecurrent margin reference unit sets the rotor based q-axis current marginreference to “0” in a steady state or when current is not limited.
 15. Amethod to control an inverter control apparatus that includes a currentsensor, a voltage sensor and a controller and controls an inverterhaving a DC-link voltage pulsating at double a system frequency, themethod comprising: the inverter control apparatus sensing an outputcurrent and a DC-link voltage of the inverter; the inverter controlapparatus calculating an average of a periodically varying rotor basedq-axis current boundary value on a basis of the output current and theDC-link voltage; the inverter control apparatus generating a currentreference on the basis of the average of the rotor based q-axis currentboundary value; and the inverter control apparatus driving a three-phasemotor on the basis of the current reference.
 16. The method according toclaim 15, wherein the inverter control apparatus generating the currentreference comprises estimating at least one of a system angle, a systemfrequency, a double system angle and a double system frequency on thebasis of the DC-link voltage.
 17. The method according to claim 16,wherein the inverter control apparatus generating the current referencefurther comprises generating a rotor based q-axis current reference in asine squared form, which is synchronized with the system angle, on thebasis of the system angle.
 18. The method according to claim 17, whereinthe inverter control apparatus generating the current reference furthercomprises generating a rotor based d-axis current reference on the basisof the average of the rotor based q-axis current boundary value and therotor based q-axis current reference.
 19. The method according to claim16, wherein the inverter control apparatus estimating at least one ofthe system angle, the system frequency, the double system angle and thedouble system frequency comprises: squaring the DC-link voltage togenerate a DC-link voltage square; generating a double system frequencycomponent value having a frequency twice the system frequency on thebasis of the DC-link voltage square and the double system frequency;generating a 90° phase-retarded value having a phase retarded by 90°from the double system frequency component value; generating asynchronous reference frame based d-axis virtual voltage and asynchronous reference frame based q-axis virtual voltage, which areconstants and have a phase difference therebetween, on the basis of the90°-phase-retarded value, a value obtained by multiplying the doublesystem frequency component value by “−1”, and the double system angle;and generating at least one of the system angle, the system frequency,the double system angle, and the double system frequency on thesynchronous reference frame based d-axis virtual voltage and constant“0”.
 20. The method according to claim 17, wherein the inverter controlapparatus generating the rotor based q-axis current reference comprises:generating a unit sine square waveform having the system angle;generating a q-axis current reference corresponding to the output torquecommand value; multiplying the unit sine square waveform by the q-axiscurrent reference to generate a q-axis current reference in a sinesquared form; generating a current gain that makes the average of theoutput torque command value equal to the average of a current referencemodified torque generated according to the rotor based q-axis currentreference; and multiplying the q-axis current reference in a sinesquared form by the current gain to generate a rotor based q-axiscurrent reference.
 21. The method according to claim 20, wherein thecurrent gain setting unit sets the current gain to “2”.
 22. The methodaccording to claim 5, wherein the inverter control apparatus generatingthe rotor based d-axis current reference comprises: generating a rotorbased d-axis voltage boundary value corresponding to a maximuminstantaneous voltage that can be applied to a d axis on the basis ofthe DC-link voltage; generating a unit gain that changes a voltage valueinto a current value; generating a rotor based q-axis current boundaryvalue on the basis of the rotor based d-axis voltage boundary value andthe unit gain; subtracting the rotor based q-axis current reference fromthe average of the rotor based q-axis current boundary value to generatea rotor based q-axis margin value; generating a rotor based q-axiscurrent margin reference on the basis of the output torque commandvalue; generating an error value by subtracting the rotor based q-axiscurrent margin reference from the rotor based q-axis current marginvalue; and sequentially applying the error value to a low pass filterand a proportional integrator to generate a rotor based d-axis currentreference.
 23. The method according to claim 22, wherein the invertercontrol apparatus generating the rotor based d-axis current referencecomprises setting the rotor based d-axis current reference to a positivevalue such that the rotor based d-axis current reference is set to anegative value when generated torque is insufficient due to currentlimitation.
 24. The method according to claim 22, wherein the invertercontrol apparatus generating the rotor based d-axis current referencecomprises setting the rotor based q-axis current margin reference to “0”in a steady state or when current is not limited.
 25. A controller tocontrol an apparatus comprising: a current sensor to sense an outputcurrent of the apparatus; a voltage sensor to sense a DC-link voltage ofthe apparatus; and a processor to generate an average of a periodicallyvarying rotor based q-axis current boundary value based on the sensedoutput current and the sensed DC-link voltage and to output a currentreference based on the generated average of the rotor based q-axiscurrent boundary value.
 26. A method to control an inverter, the methodcomprising: sensing an output current and a DC-link voltage of theinverter; calculating an average of a periodically varying rotor basedq-axis current boundary value on a basis of the sensed current and theDC-link voltage; generating a current reference on a basis of thecalculated and driving a three-phase motor on the basis of the generatedcurrent reference.